This invention relates to hydrostatic piston-and-cylinder machines, which may be pumps or motors. More specifically it relates to machines of this type in which the pistons are constrained to move along their respective cylinders by means of a cam having a sinuous track which is followed by a cam follower of circular profile. A common form for such machines uses a ball for each piston, the ball also acting as the cam follower but sometimes the ball is backed by a sealing element of cylindrical form which is constrained to move up and down the cylinder with the ball; sometimes again the piston is cylindrical in form and has a cam follower wheel mounted for rotation in a yoke in the end of the piston. The invention includes these variants within its scope but for convenience it will be described hereafter in relation to the ball-piston form of these machines.
These machines may be of the rotational type, as shown for instance in the specification of French Pat. No. 1,456,704, with the cylinders arranged radially and the pistons caused to stroke in the cylinders by a peripheral or an internal circular cam. Alternatively the cylinders may be arrayed with their axes in a cylindrical surface, as shown for instance in the specification of U.S. Pat. No. 2,617,360 with the pistons engaging the edge of an arcuate cam; in this form the cylinder block may embrace a relatively small part of the total circumference of the cam and there may be no provision for continuous rotation. Alternatively again the cylinder axes may lie in a plane with the pistons engaging a linear cam to provide a linear hydrostatic actuator or pump as shown in the specification of United Kingdom Pat. No. 961339. All these variants also are within the scope of the invention, but for convenience it will be described in relation to a machine with radial cylinders, and pistons engaging an external cam surrounding the cylinder block, the machine being adapted for continuous rotation.
The cam profile may have one or more complete lobes accommodated within the complete 360.degree. circumference. A lobe provides for one complete to and fro excursion of each piston in its cylinder. Each lobe has two half-lobes each causing the piston to make a stroke in one direction. Alternate half-lobes produce strokes of the pistons alternately in different directions.
As with all machines where hardened bodies are in rolling contact and subjected to high loading, the inter-engaging surfaces are subjected to high Hertzian stresses, and these stresses are enhanced where there is high mutual convexity as compared with the case where there is a "wrap-round" effect, the outer race of a ball bearing for instance.
In the case of machines according to the invention these stresses are enhanced in the cam crest regions as compared with the cam trough regions. It is therefore advantageous to have as large a radius of curvature as possible in these regions of the cam, even at the expense of a substantially smaller radius of curvature at the trough regions because the increased wrap-round effect increases the size of the effective contact patch between the ball piston and the cam track, for any given normal loading, so long as this is not carried to the point where unacceptable accelerations would be imposed on the ball pistons in traversing the trough regions of the cam.
It is convenient to describe the cam profile in terms of the curves of motion which it imposes upon the ball pistons, more specifically curves in which the velocity of a reference point on the piston is represented by the vertical axis and progress of the piston along the cam track by the horizontal axis (which, for a given constant speed of such progress, can be regarded as representing time). For each stroke of a piston the curve will rise from zero to a maximum velocity from which it must fall to zero again before the end of the stroke. The elementary form of this curve is an isosceles triangle representing constant acceleration followed by constant deceleration, at the same rate.
Since time x velocity = distance, it follows that the area beneath such a curve, for a stroke of the piston, represents the length of the stroke. Therefore in comparing similar machines having different stroke velocity regimes the different curves must have their velocity values adjusted to bring the areas under the curves into equality.